/*
 *  Copyright 2017 PayPal
 *
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *  http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

package org.squbs.pattern.timeoutpolicy

object MathUtil {
  /**
   * porting from org/apache/commons/math3/special/Erf.java
   * @param x the value
   * @return t such that x = erf(t)
   */
  def erfInv(x: Double):Double = {
    var w = - math.log((1.0 - x) * (1.0 + x))
    var p = 0.0

    if (w < 6.25) {
      w = w - 3.125
      p =  -3.6444120640178196996e-21
      p =   -1.685059138182016589e-19 + p * w
      p =   1.2858480715256400167e-18 + p * w
      p =    1.115787767802518096e-17 + p * w
      p =   -1.333171662854620906e-16 + p * w
      p =   2.0972767875968561637e-17 + p * w
      p =   6.6376381343583238325e-15 + p * w
      p =  -4.0545662729752068639e-14 + p * w
      p =  -8.1519341976054721522e-14 + p * w
      p =   2.6335093153082322977e-12 + p * w
      p =  -1.2975133253453532498e-11 + p * w
      p =  -5.4154120542946279317e-11 + p * w
      p =    1.051212273321532285e-09 + p * w
      p =  -4.1126339803469836976e-09 + p * w
      p =  -2.9070369957882005086e-08 + p * w
      p =   4.2347877827932403518e-07 + p * w
      p =  -1.3654692000834678645e-06 + p * w
      p =  -1.3882523362786468719e-05 + p * w
      p =    0.0001867342080340571352 + p * w
      p =  -0.00074070253416626697512 + p * w
      p =   -0.0060336708714301490533 + p * w
      p =      0.24015818242558961693 + p * w
      p =       1.6536545626831027356 + p * w
    } else if (w < 16.0) {
      w = math.sqrt(w) - 3.25
      p =   2.2137376921775787049e-09
      p =   9.0756561938885390979e-08 + p * w
      p =  -2.7517406297064545428e-07 + p * w
      p =   1.8239629214389227755e-08 + p * w
      p =   1.5027403968909827627e-06 + p * w
      p =   -4.013867526981545969e-06 + p * w
      p =   2.9234449089955446044e-06 + p * w
      p =   1.2475304481671778723e-05 + p * w
      p =  -4.7318229009055733981e-05 + p * w
      p =   6.8284851459573175448e-05 + p * w
      p =   2.4031110387097893999e-05 + p * w
      p =   -0.0003550375203628474796 + p * w
      p =   0.00095328937973738049703 + p * w
      p =   -0.0016882755560235047313 + p * w
      p =    0.0024914420961078508066 + p * w
      p =   -0.0037512085075692412107 + p * w
      p =     0.005370914553590063617 + p * w
      p =       1.0052589676941592334 + p * w
      p =       3.0838856104922207635 + p * w
    } else if (!w.isInfinite) {
      w = math.sqrt(w) - 5.0
      p =  -2.7109920616438573243e-11
      p =  -2.5556418169965252055e-10 + p * w
      p =   1.5076572693500548083e-09 + p * w
      p =  -3.7894654401267369937e-09 + p * w
      p =   7.6157012080783393804e-09 + p * w
      p =  -1.4960026627149240478e-08 + p * w
      p =   2.9147953450901080826e-08 + p * w
      p =  -6.7711997758452339498e-08 + p * w
      p =   2.2900482228026654717e-07 + p * w
      p =  -9.9298272942317002539e-07 + p * w
      p =   4.5260625972231537039e-06 + p * w
      p =  -1.9681778105531670567e-05 + p * w
      p =   7.5995277030017761139e-05 + p * w
      p =  -0.00021503011930044477347 + p * w
      p =  -0.00013871931833623122026 + p * w
      p =       1.0103004648645343977 + p * w
      p =       4.8499064014085844221 + p * w
    } else {
      // this branch does not appears in the original code, it
      // was added because the previous branch does not handle
      // x = +/-1 correctly. In this case, w is positive infinity
      // and as the first coefficient (-2.71e-11) is negative.
      // Once the first multiplication is done, p becomes negative
      // infinity and remains so throughout the polynomial evaluation.
      // So the branch above incorrectly returns negative infinity
      // instead of the correct positive infinity.
      p = Double.PositiveInfinity
    }

    p * x
  }
}
